System and method for channel-adaptive antenna selection

ABSTRACT

Systems and methods that provide channel-adaptive antenna selection in multi-antenna-element communication systems are provided. In one embodiment, a method that selects a subset of receive antennas of a receiver to receive a transmitted RF signal may include, for example, one or more of the following: establishing possible subsets of the receive antennas; determining sets of channel parameter statistics corresponding to the possible subsets of the receive antennas; computing output bit error rates of the receiver, each output bit error rate being computed based on at least one set of channel parameter statistics; selecting a particular possible subset of the receive antennas based upon a criterion predicated on the computed output bit error rates; and connecting one or more RF chains of the receiver to the receive antennas of the selected particular possible subset.

RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent applicationSer. No. 10/957,398, entitled “System and Method for Antenna Selection”and filed Oct. 1, 2004, which claims priority to and claims benefit fromU.S. patent application Ser. No. 60/507,843, entitled “Antenna SelectionMethod in Multi-Antenna Communication Systems Based On Minimum Bit ErrorRate” and filed Oct. 1, 2003. This application also makes reference tothe above-mentioned applications.

This application makes reference to, claims priority to and claimsbenefit from U.S. Patent Application Ser. No. 60/519,398, entitled“Channel-Adaptive Antenna Selection Method Based Upon Minimization ofBit Error Rate” and filed Nov. 12, 2003.

The above-identified patent applications are hereby incorporated hereinby reference in their entirety.

FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

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MICROFICHE/COPYRIGHT REFERENCE

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BACKGROUND OF THE INVENTION

Most current wireless communication systems are composed of nodesconfigured with a single transmit and receive antenna. However, for awide range of wireless communication systems, it has been predicted thatthe performance, including capacity, may be substantially improvedthrough the use of multiple transmit and/or multiple receive antennas.Such configurations form the basis of “smart” antenna techniques. Smartantenna techniques, coupled with space-time signal processing, can beutilized both to combat the deleterious effects of multipath fading of adesired incoming signal and to suppress interfering signals. In this wayboth the performance and capacity of digital wireless systems inexistence or being deployed (e.g., CDMA-based systems, TDMA-basedsystems, WLAN systems, and OFDM-based systems such as IEEE 802.11a/g)maybe improved.

At least some of the impairments to the performance of wireless systemsof the type described above may be at least partially ameliorated byusing multi-element antenna systems designed to introduce a diversitygain and suppress interference within the signal reception process. Thishas been described, for example, in “The Impact of Antenna Diversity Onthe Capacity of Wireless Communication Systems”, by J. H. Winters etal., IEEE Transactions on Communications, vol. 42, no. 2/3/4, pages1740-1751, February 1994. Such diversity gains improve systemperformance by mitigating multipath for more uniform coverage,increasing received signal-to-noise ratio for greater range or reducedrequired transmit power, and providing more robustness againstinterference or permitting greater frequency reuse for higher capacity.

Within communication systems incorporating multi-antenna receivers, aset of M receive antennas may be capable of nulling up to M−1interferers. Accordingly, N signals may be simultaneously transmitted inthe same bandwidth using N transmit antennas, with the transmittedsignal then being separated into N respective signals by way of a set ofN antennas deployed at the receiver. Systems of this type are generallyreferred to as multiple-input-multiple-output (MIMO) systems, and havebeen studied extensively. See, for example, “Optimum combining forindoor radio systems with multiple users”, by J. H. Winters, IEEETransactions on Communications, vol. COM-35, no. 11, November 1987;“Capacity of Multi-Antenna Array Systems In Indoor WirelessEnvironment”, by C. Chuah et al., Proceedings of Globecom '98 Sydney,Australia, IEEE 1998, pages 1894-1899 November 1998; and “FadingCorrelation and Its Effect on the Capacity of Multi-Element AntennaSystems” by D. Shiu et al., IEEE Transactions on Communications, vol.48, no. 3, pages 502-513, March 2000.

Some multi-element antenna arrangements (e.g., some MIMOs) providesystem capacity enhancements that can be achieved using theabove-referenced configurations. Under the assumption of perfectestimates of the applicable channel at the receiver, in a MIMO systemthe received signal decomposes to M “spatially-multiplexed” independentchannels. This results in an M-fold capacity increase relative tosingle-antenna systems. For a fixed overall transmitted power, thecapacity offered by MIMOs scales linearly with the number of antennaelements. Specifically, it has been shown that with N transmit and Nreceive antennas an N-fold increase in the data rate over a singleantenna system can be achieved without any increase in the totalbandwidth or total transmit power. See, e.g., “On Limits of WirelessCommunications in a Fading Environment When Using Multiple Antennas”, byG. J. Foschini et al., Wireless Personal Communications, Kluwer AcademicPublishers, vol. 6, no. 3, pages 311-335, March 1998. In experimentalMIMO systems predicated upon N-fold spatial multiplexing, more than Nantennas are often deployed at a given transmitter or receiver. This isbecause each additional antenna adds to the diversity gain and antennagain and interference suppression applicable to all Nspatially-multiplexed signals. See, e.g., “Simplified processing forhigh spectral efficiency wireless communication employing multi-elementarrays”, by G. J. Foschini et al., IEEE Journal on Selected Areas inCommunications, vol. 17, issue 11, November 1999, pages 1841-1852.

Although increasing the number of transmit and/or receive antennasenhances various aspects of the performance of MIMO systems, theprovision of a separate RF chain for each transmit and receive antennaincreases costs. Each RF chain is generally comprised a low noiseamplifier, filter, downconverter, and analog-to-digital converter (A/D),with the latter three devices typically being responsible for most ofthe cost of the RF chain. In certain existing single-antenna wirelessreceivers, the single required RF chain may account for in excess of 30%of the receiver's total cost. It is thus apparent that as the number oftransmit and receive antennas increases, overall system cost and powerconsumption may dramatically increase.

Some attempts to address these shortcomings may be found, for example,in U.S. Patent Publication Ser. No. 20020102950 entitled “Method andapparatus for selection and use of optimal antennas in wirelesssystems”; “Capacity of MIMO systems with antenna selection”, by A.Molisch et al., Proceedings of IEEE ICC, Helsinki, Finland, June 2001,vol. 2, pp. 570-574; and “On optimum MIMO with antenna selection”, by R.S. Blum et al., IEEE Communications Letters, vol. 6, issue 8, August2002, pages 322-324, in which a subset of transmit/receive antennas areselected from a larger number of antennas. Since with N-fold spatialmultiplexing, at least N RF chains must be used, typically N out of Mtotal antennas would be chosen at the receiver and/or N out of n_(T)total antennas would be chosen at the transmitter, with M>N and n_(T)>N.

The performance of a system with antenna selection depends, for example,on the criteria used in the selection process. Different criteria usedeven under the same channel condition may well result in a differentselected subset of antennas, thereby yielding different performances.Some of the above-reference documents advocate the maximum capacitycriterion to select the antenna subset. However, capacity is anidealized quantity that may be an unachievable bound because it maynecessitate perfect coding and/or equalization and/or continuousmodulation. In practice, the equalizer is not ideal, limited coding (oreven no coding) and quantized modulation is used.

BRIEF SUMMARY OF THE INVENTION

Some embodiments according to some aspects of the present invention mayrelate to systems and methods that provide channel-adaptive antennaselection in multi-antenna-element communication systems.

In one embodiment according to some aspects of the present invention, asystem that selects N antenna elements in an M-antenna-elementtransmitter or an M-antenna-element receiver, in which N is less than M,may include, for example, M antenna elements in the M-antenna-elementtransmitter or the M-antenna-element receiver, N RF chains, and a switchcoupled to the N RF chains. The M-antenna-element receiver may computean output bit error rate for each possible N antenna element subset ofthe M antenna elements. Each output bit error may be computed based onat least one set of channel parameter statistics. The M-antenna-elementreceiver may select the particular N antenna element subset based on acriterion predicated on the computed output bit error rates. In responseto the selection of the particular N antenna element subset based on thecriterion, the switch may couple the N RF chains to the N antennaelements of the particular N antenna element subset.

In another embodiment according to some aspects of the presentinvention, a method that selects a subset of receive antennas of areceiver to receive a transmitted RF signal may include, for example,one or more of the following: establishing possible subsets of thereceive antennas; determining sets of channel parameter statisticscorresponding to the possible subsets of the receive antennas; computingoutput bit error rates of the receiver, each output bit error rate beingcomputed based on at least one set of channel parameter statistics;selecting a particular possible subset of the receive antennas basedupon a criterion predicated on the computed output bit error rates; andconnecting one or more RF chains of the receiver to the receive antennasof the selected particular possible subset.

In another embodiment according to some aspects of the presentinvention, a method that selects a subset of transmit antennas of atransmitter to transmit an RF input signal as a plurality of RF outputsignals that are subsequently received by a receiver, may include, forexample, one or more of the following: establishing possible subsets ofthe transmit antennas; determining sets of channel parameter statisticscorresponding to the possible subsets of the transmit antennas;selecting transmission modes respectively corresponding to the sets ofchannel parameter statistics; computing output bit error rates of thereceiver, each output bit error rate being computed based on at leastone set of channel parameter statistics and at least one selectedtransmission mode; selecting a particular possible subset of thetransmit antennas based on a criterion predicated on at least thecomputed output bit error rates; and connecting one or more RF chains ofthe transmitter to the transmit antennas of the selected particularpossible subset.

In yet another embodiment according to some aspects of the presentinvention, in a communication system including a transmitter and areceiver, the transmitter including transmit antennas adapted totransmit a set of spatially-multiplexed RF output signals through achannel using two or more transmit RF chains, the receiver includingreceive antennas adapted to receive the set of spatially-multiplexed RFoutput signals and adapted to responsively generate a set ofspatially-multiplexed received RF signals that is processed by two ormore receive RF chains, an antenna selection method may include, forexample, one or more of the following: establishing possible subsets ofthe transmit antennas and possible subsets of the receive antennas;determining sets of channel parameter statistics corresponding tocombinations of the possible subsets of the transmit antennas and thepossible subsets of the receive antennas; selecting transmission modesrespectively corresponding to the sets of channel parameter statistics;computing output bit error rates of the receiver, each output bit errorrate being computed based on at least one set of channel parameterstatistics and a corresponding selected transmission mode; selecting aparticular possible subset of the transmit antennas and a particularpossible subset of the receive antennas based on a criterion predicatedon at least the computed output bit error rates; connecting the two ormore of the transmit RF chains to the selected particular possiblesubset of the transmit antennas; and connecting the two or more receiveRF chains to the selected particular possible subset of the receiveantennas.

In yet still another embodiment according to some aspects of the presentinvention, in a communication system including a transmitter and areceiver, the transmitter including transmit antennas adapted totransmit a set of RF output signals through a channel using one or moretransmit RF chains, the receiver including receive antennas adapted toreceive the set of RF output signals and adapted to responsivelygenerate a set of received RF signals that is processed by one or morereceive RF chains, an antenna selection method may include, for example,one or more of the following: establishing possible subsets of thetransmit antennas and possible subsets of the receive antennas;determining sets of channel parameter statistics corresponding tocombinations of the possible subsets of the transmit antennas and thepossible subsets of the receive antennas; selecting transmission modesrespectively corresponding to the sets of channel parameter statistics;computing output bit error rates of the receiver, each output bit errorrate being computed based on at least one set of channel parameterstatistics and a corresponding selected transmission mode; selecting aparticular possible subset of the transmit antennas and a particularpossible subset of the receive antennas based on a criterion predicatedon at least the computed output bit error rates; connecting the one ormore of the transmit RF chains to the selected particular possiblesubset of the transmit antennas; and connecting the one or more receiveRF chains to the selected particular possible subset of the receiveantennas.

These and other features and advantages of some embodiments according tosome aspects of the present invention may be appreciated from a reviewof the following detailed description, along with the accompanyingfigures in which like reference numerals refer to like parts throughout.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-B show an embodiment of a conventional MIMO communicationsystem.

FIGS. 2A-B show an embodiment of a MIMO system according to some aspectsof the present invention.

FIG. 3 shows an embodiment of an SM-MIMO-OFDM system according to someaspects of the present invention.

FIGS. 4A-B show flowcharts illustrating embodiments of an antennaselection method according to some aspects of the present invention.

FIG. 5 shows a graph illustrating exemplary performance resultsaccording to some aspects of the present invention.

FIG. 6 shows an embodiment of an SC-MIMO-OFDM system according to someaspects of the present invention.

FIG. 7 shows an embodiment of a receiver in a DS-SS SIMO systemaccording to some aspects of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

I. Overview of Some Aspects of the Present Invention

Some embodiments according to some aspects of the present invention mayrelate to communication systems that use a transmitter and/or a receiverthat have multiple antenna elements.

Some embodiments according to some aspects of the present invention mayrelate to systems and methods that provide channel-adaptive antennaselection in multi-antenna-element communication systems.

Some embodiments according to some aspects of the present invention maybe implemented to facilitate a selection of a subset of antenna elementsin one or more multi-antenna wireless communication devices based on acriterion predicated, at least in part, on computed output bit errorrates.

Some embodiments according to some aspects of the present invention maybe implemented to facilitate the selection of a subset of antennaelements in one or more multi-antenna wireless communication devices soas to minimize or to optimize, for example, a bit error rate (BER).

Some embodiments according to some aspects of the present invention maybe implemented to facilitate a channel-adaptive selection of a subset ofantenna elements in one or more multi-antenna wireless communicationdevices based on a criterion predicated, at least in part, on computedoutput bit error rates.

Some embodiments according to some aspects of the present invention mayenable the use of a greater number of antenna elements than the numberof radio frequency (RF) chains. Some embodiments according to someaspects of the present invention may enhance system performance in acost-effective manner.

Some embodiments according to some aspects of the present invention maybe employed to select a subset of antenna elements of a multi-antennatransmitter to transmit a signal and/or to select a subset of antennaelements of a multi-antenna receiver to receive a signal.

Some embodiments according to some aspects of the present invention mayprovide that a selection of the subset of antenna elements ispredicated, at least in part, upon a criterion based, at least in part,on at least computed output bit error rates.

Some embodiments according to some aspects of the present invention mayprovide that the selection of the subset of antenna elements ispredicated, at least in part, upon a minimization of a BER.

Some embodiments according to some aspects of the present invention maybe applicable to communications systems that employ, for example, codedivision multiple access signals, spread spectrum signals, singlecarrier signals, multiple carrier signals, orthogonal frequencydivisional multiplexed signals, ultra-wideband signals, space-timediversity signals and spatially-multiplexed signals.

Some embodiments according to some aspects of the present invention mayprovide that a selection of the subset of antenna elements bepredicated, at least in part, upon a minimization of a BER based on, forexample, parameters (e.g., statistical parameters) related to one ormore communication channels. Some embodiments according to some aspectsof the present invention may provide that a selection of a subset ofantenna elements be predicated upon minimization of a BER that iscomputed based, at least in part, on parameter statistics of one or moreapplicable communication channels.

Some embodiments according to some aspects of the present invention maybe used for antenna selection in a multiple-input-multiple-output (MIMO)communication system. The MIMO communication system may provide, forexample, a transmitter that broadcasts a plurality (N) ofspatially-multiplexed signals through N transmit antenna elementsselected from a set of n_(T) antenna elements, where n_(T)>N. The MIMOcommunication system may provide, for example, a receiver in which Nreceive antenna elements, selected from a total of M elements where M>N,form a number of output signals equal to the number ofspatially-multiplexed signals. The output signals are in turn providedto corresponding RF chains for processing at baseband. Thus, someembodiments according to some aspects of the present invention mayadvantageously permit minimization of BER (e.g., channel-adaptiveminimization of BER) and/or reduction of RF signal processing costswithin multiple-antenna systems.

Some embodiments according to some aspects of the present invention mayprovide a transmitter including one or more RF chains and a particularplurality of transmit antennas, which may be all or less than all of thetransmit antennas of the transmitter. Some embodiments according to someaspects of the present invention may provide a system and/or a methodthat, for example, selects a subset of a particular plurality oftransmit antennas, the subset transmitting an RF input signal, forexample, as a plurality of RF output signals subsequently received, forexample, by a receiver. A plurality of possible subsets (e.g., all orless than all of the possible subsets comprising a particular number oftransmit antennas or other types of grouping characteristics) of theparticular plurality of transmit antennas may be established. Sets ofchannel parameter statistics or other parameters corresponding to thepossible subsets of the particular plurality of transmit antennas maythen be determined. Transmission modes or other types of modescorresponding to respective sets of channel parameter statistics may beselected. Transmission modes may include, for example, a modulationlevel and/or a coding rate. A plurality of BERs (e.g., output BERs) ofthe receiver, for example, may be computed. Each of the plurality ofoutput BERs, for example, may be computed based, at least in part, upon,for example, a set of channel parameter statistics and/or correspondingselected transmission modes. A possible subset of the particularplurality of transmit antennas may be selected based upon, for example,criteria predicated, at least in part, upon the output BERs and/or theselected transmission modes. One or more RF chains may then be connectedto the transmit antenna or antennas of the selected possible subset ofthe particular plurality of transmit antennas.

Some embodiments according to some aspects of the present invention mayprovide for channel parameter statistics that may include, for example,first-order statistics, second-order statistics or higher-orderstatistics. Channel parameter statistics may include, for example, oneor more of the following: an output signal-to-noise ratio, an outputsignal-to-interference-and-noise ratio, a likelihood ratio (e.g., alog-likelihood ratio), a Euclidean distance in a signal constellation,for example, of a receiver. Channel parameter statistics may becomputed, for example, over a frequency domain or a time domain.

Some embodiments of an antenna selection method according to someaspects of the present invention may be used with different types ofmulti-antenna communication systems. In particular embodiments, someembodiments of an antenna selection method according to some aspects ofthe present invention may be applied, for example, to a multi-antennareceiver within a “single channel” (SC) system (e.g., a system withoutspatial multiplexing), to a multi-antenna transmitter in a singlechannel system, or to the transmitter and/or receiver of a MIMO systememploying spatial multiplexing (SM) or single channel.

Some embodiments according to some aspects of the present invention mayprovide, for example, a number N of receive antenna elements that areselected from a set of M available antenna elements (where M>N) suchthat the selected subset of antenna elements minimizes the BER, forexample, when various channel parameter statistics are taken intoaccount. This may be effected by establishing possible subsets of aplurality of transmit antennas and possible subsets of the M receiveantennas. The method further includes determining plural sets of channelparameter statistics corresponding to combinations of ones of thepossible subsets of the plurality of transmit antennas and ones of thepossible subsets of the plurality of receive antennas. Pluraltransmission modes respectively corresponding to the plural sets ofchannel parameter statistics are then selected. In addition, pluraloutput bit error rates of the receiver are computed based at least inpart upon one of the plural sets of channel parameter statistics and acorresponding one of the plural transmission modes. One of the possiblesubsets of the plurality of transmit antennas and one of the possiblesubsets of the plurality of receive antennas are then selected basedupon criterion predicated at least in part upon the plural output biterror rates and the plural transmission modes. The method furtherincludes connecting one or more of the transmit RF chains to the one ofthe possible subsets of the plurality of transmit antennas and the oneor more receive RF chains to the one of the possible subsets of theplurality of receive antennas.

Some embodiments according to some aspects of the present invention mayprovide for a criterion that is based on, for example, one or more ofthe following: an output bit error rate; a transmission mode; aminimization of an output bit error rate; a maximization of a data rate;a maximization of a data rate within a first stage of a receiver; and aminimization of an output bit error rate in a second stage of areceiver.

In the case of a single-channel or spatially-multiplexed MIMO systemwhich uses multiple RF chains at transmit and/or receiver side, certainbaseband weighting and combining arrangements may be incorporated withinthe transmitter (e.g., precoding) and/or receiver together with theselection method. For example, the baseband weights and antennaselection may be both designed such that they contribute to minimize theBER. In another example, the baseband weights may be designed tomaximize, for example, an output signal-to-noise ratio (SNR), asignal-to-interference-and-noise ratio (SINR), or a capacity whileminimizing BER through appropriate antenna selection.

Some embodiments according to some aspects of the present invention aredirected to a channel-adaptive method and/or system for antennaselection based upon minimizing the BER for use in multi-antennasystems, including, for example, N-fold spatially-multiplexedmulti-antenna systems. To facilitate appreciation of some embodimentsaccording to some aspects of the present invention, an overview isprovided of exemplary architectures that may implement antenna selectionwithin multi-antenna systems. After the overview, additional detailsrelating to system and methods for channel-adaptive antenna selectionbased on, for example, minimization of BER may be presented.

II. Architecture for Antenna Selection

Some embodiments according to some aspects of the present invention maybe implemented in wireless communication systems in which a smallernumber of RF chains are used within a transmitter and/or receiver thanthe number of transmit/receiver antennas utilized. In some embodimentsaccording to some aspects of the present invention, a number N ofreceive antenna elements is selected out of a total number of elementsM, where M>N. This forms N RF output signals, which are then passedthrough N RF chains. In an exemplary implementation, each RF chainincludes, for example, a filter, downconverter, and A/D converter. Theoutput signals produced by the A/D converter of each RF chain are thendigitally processed to generate the N spatially-multiplexed outputsignals. By performing the requisite selection of a subset of antennasat RF, an N-fold spatially-multiplexed system having more than N receiveantennas, but only N RF chains, can be realized at a cost similar tothat of a system having N receive antennas. Accordingly, receiverperformance may be improved through use of additional antennas atrelatively low cost.

A similar technique can be used at a transmitter incorporating N RFchains and a number n_(T) of transmit antennas that is greater than N.In an exemplary implementation the N RF chains are followed by a switchwhich connects each of them to a subset of N transmit antennas selectedout of n_(T). As at the receiver, by performing such selection of asubset of antennas at RF, an N-fold spatially-multiplexed system havingmore than N transmit antennas, but only N RF chains, can be realized ata cost similar to that of a system having N transmit antennas and N RFchains. Accordingly, transmitter performance may be improved through useof additional antennas at relatively low cost.

A. Spatial Multiplexing

According to some embodiments according to some aspects of the presentinvention, spatial multiplexing (SM) provides a mode of signaltransmission predicated upon the use of multiple antennas at both atransmitter and a receiver in such a way that the bit rate of a wirelessradio link may be increased without correspondingly increasing power orbandwidth consumption. In the case in which N antennas are used at botha transmitter and a receiver, an input stream of information symbolsprovided to the transmitter is divided into N independent substreams.Spatial multiplexing contemplates that each of these substreams willoccupy the same “channel” (e.g., a time slot, a frequency or a code/keysequence) of the applicable multiple-access protocol. Within thetransmitter, each substream is separately applied to the N transmitantennas and propagated over an intervening multipath communicationchannel to a receiver. The composite multipath signals are then receivedby a receive array of N receive antennas deployed at the receiver. Atthe receiver, a “spatial signature” defined by the N phases and Namplitudes arising at the receive antenna array for a given substream isthen estimated. Signal processing techniques are then applied in orderto separate the received signals, which permit the original substreamsto be recovered and synthesized into the original input symbol stream.The principles of spatially-multiplexed communication and exemplarysystem implementations are further described in, for example, “Optimumcombining for indoor radio systems with multiple users”, by J. H.Winters, IEEE Transactions on Communications, vol. COM-35, no. 11,November 1987, which is hereby incorporated herein by reference in itsentirety.

B. Conventional MIMO System

Some aspects of the present invention may be more fully elucidated byfirst considering a conventional MIMO communication system, which isillustratively represented by FIG. 1. As shown, the MIMO system 100 ofFIG. 1 includes a transmitter 110 depicted in FIG. 1A and a receiver 130depicted in FIG. 1B. The transmitter 110 and receiver 130 include a setof T transmit RF chains and a set of R receive RF chains, respectively,which are configured to transmit and receive a group of Nspatially-multiplexed signals. Within the system 100 it may be assumedthat either (i) T is greater than N and R is equal to N; (ii) T is equalto N and R is greater than N; or (iii) both T and R are greater than N.

Referring to FIG. 1A, an input signal S to be transmitted, whichtypically includes of a stream of digital symbols, is demultiplexed bydemultiplexer 102 into N independent substreams S_(1, 2 . . . , N). Thesubstreams S_(1, 2 . . . , N) are then sent to digital signal processor(DSP) 105, which generates a set of T output signals T_(1, 2 . . . , T).The T output signals T_(1, 2 . . . , T) are typically generated from theN substreams S_(1, 2 . . . , N) by weighting (e.g., multiplying by acomplex number) each of the N substreams S_(1, 2 . . . , N) by Tdifferent weighting coefficients to form NT substreams. These N·Tsubstreams are then combined in order to form the T output signalsT_(1, 2 . . . , T). The T output signals T_(1, 2 . . . , T) are thenconverted to T analog signals A_(1, 2 . . . , T) using a set of Tdigital-to-analog (D/A) converters 108. Each of the T analog signalsA_(1, 2 . . . , T) is then upconverted to the applicable transmitcarrier RF frequency within a mixer 112 by mixing with a signal providedby a local oscillator 114. The resulting set of T RF signals (e.g.,RF_(1, 2 . . . , T)) are then amplified by respective amplifiers 116 andtransmitted by respective antennas 118.

Referring now to FIG. 1B, the RF signals transmitted by the transmitter110 are received by a set of R receive antennas 131 deployed at thereceiver 130. Each of the R signals received by an antenna 131 isamplified by a respective low noise amplifier 133 and passed through afilter 135. The resultant filtered signals are then each downconvertedfrom RF to baseband using mixers 137, each of which is provided with asignal from local oscillator 138. Although the receiver of FIG. 1B isconfigured as a homodyne receiver, a heterodyne receiver characterizedby an intermediate IF frequency could also be used. The respective Rbaseband signals produced by the mixers 137 are then converted todigital signals using a corresponding set of R analog-to-digital (A/D)converters 140. The resulting R digital signals D_(1, 2 . . . , R) arethen weighted and combined using digital signal processor 142 to form Nspatially-multiplexed output signals S′_(1, 2 . . . , N) which compriseestimates of the transmitted signals S_(1, 2 . . . , N). The N outputsignals S′_(1, 2 . . . , N) are then multiplexed using a multiplexer 155in order to generate an estimate 160 (S′) of the original input signalS.

C. Antenna Selection at RF in Spatially-Multiplexed CommunicationSystems

Turning now to FIG. 2, there is shown a block diagram of a MIMOcommunication system 200 having a transmitter 210 and receiver 250configured to effect N-fold spatial multiplexing using only Ntransmit/receive RF chains, even though more than N transmit/receiveantennas are respectively deployed at the transmitter 210 and receiver250. Specifically, the transmitter 210 includes a set of MT transmitantennas 240 and the receiver includes a set of MR receive antennas 260,some embodiments according to some aspects of the present invention mayprovide that MT and/or MR are greater than or equal to N. For example,(i) MT is greater than N and MR is equal to N; (ii) MT is equal to N andMR is greater than N; or (iii) both MT and MR are greater than N.

As shown in FIG. 2A, an input signal S to be transmitted isdemultiplexed by demultiplexer 202 into N independent substreamsSS_(1, 2 . . . , N). The substreams SS_(1, 2 . . . , N) are thenconverted to N analog substreams AS_(1, 2 . . . , N) using acorresponding set of D/A converters 206. Next, the N analog substreamsAS_(1, 2 . . . , N) are upconverted to the applicable transmit carrierRF frequency using a set of mixers 212 provided with the signal producedby a local oscillator 214. The resultant N RF signals (e.g.,RF_(1, 2 . . . , N)) are then each connected to a selected subset of Ntransmit antenna elements by a switch 218. The switch 218 connects N RFsignals (e.g., RF_(1, 2 . . . , N)) to a set of N transmit antennas fromthe MT available transmit antennas 240, thereby yielding a set of Noutput signals. A corresponding set of N amplifiers 234 then amplifythese N output signals, with the amplified output signals then beingtransmitted using the N selected transmit antennas 240. In anotherexample, the amplifiers 234 may be located before the switch 218. Inthis configuration, a total of only N amplifiers is needed instead of atotal of MT if one amplifier is placed at each of the MT antennas. Theselection of the N antennas is generated so as to minimize the BER ofthe output signal at the receiver.

Referring to FIG. 2B, the N RF signals transmitted by the transmitter210 are received by the set of MR receive antennas 260 deployed at thereceiver 250. Each of the MR received signals is amplified by arespective low noise amplifier (LNA) 264 and then a subset N of them isconnected to a set of N RF chains by a switch 276 in order to form a setof N RF signals which are passed through a corresponding set of Nfilters 280. In another example, the low noise amplifier 264 may belocated after the switch 276 such that the total number of used LNA is Ninstead of MR if one LNA is placed at all MR receive antenna elements.The resulting N filtered signals are then downconverted to basebandusing a set of N mixers 282, each of which is provided with a carriersignal produced by a local oscillator 284. Although the receiver 250 isrealized as a homodyne receiver in the embodiment of FIG. 2B, it couldalso be implemented as a heterodyne receiver characterized by anintermediate IF frequency. (In fact, any of the embodiments according tosome aspects of the present invention may incorporate, for example,homodyne configurations or heterodyne configurations). The N basebandsignals produced by the mixers 282 are then converted to digital signalsvia a corresponding set of N A/D converters 286. The N digital signalsare then further processed using digital signal processor 288 to formthe N spatially-multiplexed output signals SS′_(1, 2 . . . , N), whichare the estimates of the N independent substreams SS_(1, 2 . . . , N).The N output signals SS′_(1, 2 . . .) , N are then multiplexed via amultiplexer 292 in order to generate the output signal S′, which is anestimate of the input signal S.

In some embodiments according to some aspects of the present invention,a baseband weighting and combining (e.g., a “preceding”) arrangement maybe added at the transmitter side for use in conjunction with the antennaselection method discussed below. In this case a DSP block is placedbetween the demultiplexer 202 and the D/A converters 206, such that theN independent substreams SS_(1, 2 . . . , N) are weighted by complexcoefficients and combined to form a set of N output signals. These Noutput signals are then converted into analog signalsAS_(1, 2 . . . , N) using the corresponding set of D/A converters 206.

In some embodiments according to some aspects of the present invention,space-time coding can be added at the transmitter side for use inconjunction with an exemplary antenna selection method. In this case,the demultiplexer 202 is replaced by a DSP block which processes theinput signal S over the space and time domain to form a set of N outputsignals. These N output signals are then converted into analog signalsAS_(1, 2 . . . , N) using the corresponding set of D/A converters 206.Among the two most commonly used space-time techniques are 1) theinsertion of a time delay (or equivalently a phase-shift) on one or moreof the N output signals and 2) the use of the transmit diversitytechnique described in, for example, “A simple transmit diversitytechnique for wireless communications”, by S. M. Alamouti, IEEE Journalon Selected Areas in Communications, vol. 16, issue 8, October 1998,pages 1451-1458, which is hereby incorporated herein by reference in itsentirety.

Space-time coding techniques may be applicable, for example, to the SCMIMO systems and/or systems designed to yield diversity gain. Precodingtechniques may be applicable, for example, to SC-based orspatial-multiplexing-based MIMO systems or systems designed to yieldboth data rate and diversity gains.

III. Channel-Adaptive Antenna Selection Method and/or System at RF Basedon Minimum Bit Error Rate

A. Overview

Some embodiments according to some aspects of the present inventionrelate, for example, to a channel-adaptive antenna selection methodand/or a channel-adaptive antenna selection system in a multi-antennacommunication system predicated on, for example, minimizing a bit errorrate. In some embodiments according to some aspects of the presentinvention, a subset of antenna elements is selected to transmit and/orreceive the signals such that the bit error rate is minimized, forexample, in a communication system with multiple antennas. Someembodiments according to some aspects of the present invention mayprovide, in a communication system with multiple antennas, that a subsetof antenna elements is selected to transmit and/or receive the signalssuch that the bit error rate is minimized, for example, over time in thepresence of variation in one or more applicable communication channels.Some embodiments according to some aspects of the present invention maybe used for antenna selection at the transmitter when multiple antennasare used for transmission. Some embodiments according to some aspects ofthe present invention can be used for antenna selection at the receiverwhen multiple antennas are used for reception.

Some embodiments according to some aspects of the present invention maybe applicable to, for example, (i) receivers using multiple antennas inwhat are referred to herein as single channel systems (e.g., systemlacking spatial multiplexing); (ii) transmitters using multiple antennasin single channel systems; and (iii) systems in which a smaller numberof RF chains are used at the transmitter and/or receiver than the numberof transmit and/or receiver antennas in a MIMO system with spatialmultiplexing or single-channel.

Some embodiments according to some aspects of the present invention willbe described hereinafter with reference to FIGS. 3-7 within thefollowing exemplary contexts: 1) a MIMO system with spatial multiplexingin which a smaller number of RF chains are used at the transmitter andreceiver than the number of transmitter/receiver antennas; 2) asingle-channel MIMO system without spatial multiplexing in which asmaller number of RF chains are used at the transmitter and receiverthan the number of transmitter/receiver antennas; and 3) asingle-channel SIMO system without spatial multiplexing containing areceiver using multiple antenna elements. Some embodiments according tosome aspects of the present invention may also be employed in the caseof a single-channel (SC) multiple-input-single-output (MISO) systemwithout spatial multiplexing in which a transmitter utilizes multipleantenna elements.

For illustrative purposes, the following exemplary examples aredescribed with reference to systems utilizing OFDM modulation (e.g.,following the 802.1-1a WLAN standard) or to systems based upon a directsequence spread spectrum (DS-SS) (e.g., following the WCDMA standard).In certain embodiments according to some aspects of the presentinvention, the processing capabilities of the DS-SS receiver may beextended to cover the spatial domain through incorporation of aspace-time Rake receiver operative to combine multi-path “taps”corresponding to both the temporal and spatial domains. This extensionillustrates that the techniques described herein may be generalized tovirtually any system employing, for example, temporal and/or frequencydomain processing in a frequency-selective fading environment.

B. Antenna Selection in a SM-MIMO-OFDM System

FIG. 3 illustratively represents the transmitter and receiver structureof an SM-MIMO-OFDM system 300 utilizing antenna selection in accordancewith an embodiment according to some aspects of the present invention.As shown, two independent sub-streams 304 (e.g., spatially-multiplexedsignals) are OFDM-modulated onto N_(t) frequency sub-carriers and passedthrough two RF chains 308 to prepare for transmission. At this point, aswitching block 312 selects two of four transmit antenna elements 316 toconnect to the two RF chains 308. Since only two out of four elements316 are selected within the transmitter 302, the number of transmit RFchains is advantageously reduced to the number of spatially-multiplexedsignals.

In the embodiment of FIG. 3, the switching block 312 containsinformation identifying the pair of antenna elements 316 to be used fortransmission at any given time. The block 312 may compute thisinformation itself (e.g., in the case where the channel 318 isreciprocal) in accordance with an algorithm based upon the minimum BERcriterion. In another example, the block 312 may receive the informationfrom the receiver 330 via a feedback path (not shown). This latterapproach may be used in the case where the channel 318 is notreciprocal, for example, in an interference-limited environment.

Within the receiver 330, a switching block 334 selects two of fourantenna elements 338 to receive incident signals transmitted by thetransmitter 302. The switching block 334 connects the two selectedantennas 338 to two RF chains 342 operative to convert the two signalsinto the digital domain for baseband processing. Then, a weight matrix346 is applied to the received signals at each tone to separate andrecover each one of the transmitted spatially-multiplexed signals.

In typical implementations the switching block 334 will be configured toitself compute which pair of antenna elements 338 should be selected forreception by executing an algorithm based upon the minimum BERcriterion. In the case where the channel is not reciprocal, the block334 may be further configured to compute which pair of antenna elements316 should be used in the transmitter 302 and to provide thisinformation to it. A description of two possible implementations of anantenna selection algorithm executable by the switching blocks 312, 334is provided with reference to FIGS. 4A and 4B.

Turning now to FIG. 4A, a flowchart is provided of an antenna selectionalgorithm 400 in which the coding/modulation mode (e.g., data rate orthroughput) is fixed or adapted on a long-term basis (e.g., adapted tothe large-scale variations of the SNR). The task of the selectionalgorithm is to select which pair of antenna elements 316 should be usedat the transmitter 302 and which pair of antenna elements 338 should beused at the receiver 330 with respect to each packet for the given mode.The selection process may assume, for example, that the channel 318 isquasi-stationary (e.g., the channel 318 is constant over the duration ofthe packet being transmitted and changes independently between twocontiguous packets). Even though the channel 318 may exhibit somefrequency selectivity, the antenna selection may be common to the entirefrequency bandwidth.

Referring to FIG. 4A, when the transmitter 302 initially powers up (step401) and the state of the channel 318 is still unknown, a default subsetof two of the antenna elements 316 is used to transmit the wirelesssignal. The receiver 330 similarly uses a default subset of two of thereceive antenna elements 338 in order to acquire synchronization. Next,channel state information (CSI) is acquired (step 402). In someembodiments according to some aspects of the present invention,operations to acquire CSI are carried out at the receiver 330. Atraining sequence composed of known symbols is sent from the transmitter302 to the receiver 330. At the receiver 330, the channel 318 isestimated based on the received signal and the known sequence ofsymbols. This operation is carried out as often as the channel 318changes, for example, at each packet realization. In order for theselection method to be performed successfully, the complete channelmatrix should be estimated over the whole frequency bandwidth (e.g., theestimation of the channel path gain from all antenna elements 316 of thetransmitter 302 to all antenna elements 338 of the receiver across alltones). Channel estimation techniques based on training sequencesapplicable to MIMO systems are described in, for example, J. J. Van deBeek et al., “On Channel Estimation in OFDM Systems”, IEEE 45thVehicular Technology Conference, vol. 2, 25-28 July 1995, pp. 815-819and A. N. Mody and G. L. Stuber, “Synchronization for MIMO OFDMSystems”, IEEE Globecom 2001, vol. 1, pp. 509-513, which are herebyincorporated herein by reference in their entirety.

Referring again to FIG. 4, mode information is acquired throughexecution of a link adaptation algorithm (step 404). In the embodimentillustrated by FIG. 4A, the mode change may occur slowly. This enables alink adaptation algorithm to be employed to decide which of the possiblemode candidates is best suited to be used in view of the long-termaverage SNR. Employment of a link adaptation algorithm may ensure that,given a mode selection criterion (e.g., a maximum data rate and aminimum transmit power), the most efficient mode is always used in viewof long-term varying channel/SNR conditions. An exemplary linkadaptation algorithm capable of being utilized withinfrequency-selective MIMO systems is described, for example, in “AdaptiveModulation and MIMO Coding for Broadband Wireless Data Networks”, by S.Catreux et al., IEEE Communications Magazine, vol. 40, No. 6, June 2002,pp. 108-115, which is incorporated herein by reference in its entirety.The mode selection may generally be independent of the method ofselecting transmitter/receiver antenna elements. The mode may beselected based exclusively upon long-term SNR statistics. Accordingly,it changes at a much slower rate than that at which the antennas areselected. In other words, the selection algorithm may select a newsubset of antennas with respect to each packet realization, while themode changes as a function of long-term SNR variations.

Steps 406, 408 and 410 are repeatedly executed in a loop until allpossible combinations of subsets of transmit/receive antenna elementshave been evaluated (step 411). For example, considering a MIMO-OFDMsystem of the type depicted in FIG. 3 (e.g., equipped with 4 transmitantenna elements 316 and 4 receive antenna elements 338), the completechannel matrix can be represented in the frequency domain at tone k by a4×4 matrix denoted by H_(k). After selection of a subset of two antennasat each side, the sub-channel matrix is reduced in size to a 2×2 matrixdenoted by {tilde over (H)}_(k). There are

$\begin{pmatrix}4 \\2\end{pmatrix} = 6$possibilities in selecting 2 elements out of a total of 4. Since theantenna selection is applied at both the transmitter 302 and receiver330, the total number of combinations possible for {tilde over (H)}_(k)is equal to 36. In the general case of a M×M MIMO system being reducedin size to a n×n MIMO system (where M>n), there are

$\begin{pmatrix}M \\n\end{pmatrix} = \frac{M!}{{n!}{\left( {M - n} \right)!}}$possibilities in selecting n antenna element from M possible elements.When the selection occurs at both a transmitter and receiver, the totalnumber of combinations for {tilde over (H)}_(k) is equal to

$\left( \frac{M!}{{n!}{\left( {M - n} \right)!}} \right)^{2}.$This corresponds to the number of iterations of the loop comprised ofsteps 406, 408 and 410. These iterations may be performed in series(e.g., reusing, common processing resources) or in parallel (e.g., atthe expense of additional processing resources). In an exemplaryexample, all possible antenna combinations could be contemporaneouslyprocessed, which might employ a separate processing resource for eachpossible antenna combination.

Each iteration in the loop comprised of steps 406, 408 and 410 effectsprocessing of one antenna subsystem. First, the 2×2 matrix {tilde over(H)}_(k) is acquired across all tones (k=1, . . . , N_(t)) for thesubsystem of interest (Step 406). The post-processingsignal-to-interference-and-noise ratio (SINR) is then computed at eachtone k and for each transmitted spatially-multiplexed signal (Step 408).The SINR can most often be found by a closed-form solution dependentupon which signal processing technique is used at the transmitter 302and/or receiver 330 (e.g., Maximum Ratio Combining (MRC), Minimum MeanSquare Error (MMSE), eigen-beamforming, and Maximum Likelihood (ML)).For example, if no spatial processing is implemented at the transmitter302 and MMSE is applied at the receiver 330, the SINR may be determinedas follows:

-   -   Compute

$\begin{matrix}{B_{k} = {{{\overset{\sim}{H}}_{k}^{H}{\overset{\sim}{H}}_{k}} + {\frac{\sigma^{2}}{\sigma_{s}^{2}}I_{2}}}} & {with} & {{I_{2} = \begin{bmatrix}1 & 0 \\0 & 1\end{bmatrix}},}\end{matrix}$

-   -    σ² and σ_(s) ² stand for noise and signal power respectively        and k=1, . . . , N_(t) (step 408-1).    -   Compute C_(k)=1/diag(B_(k) ⁻¹) this is a N×1 vector for each        k=1, . . . , N_(t) (step 408-2).    -   Compute

${SINR}_{K} = {{\frac{\sigma_{s}^{2}}{\sigma^{2}}C_{k}} - 1}$

-   -    this is a N×1 vector for each k=1, . . . , N_(t) (step 408-3).

In step 410, the SINR information is converted into BER information inview of the current mode (see, e.g., step 404). Since the BER may be acomplicated function of the channel 318 and of the coding/modulation andantenna combining techniques used, an approximation of the BER may beused. The approximation may also be a function of the channel 318 and ofthe applicable coding/modulation and antenna combining techniques. TheBER over the packet (e.g., at the output of the Viterbi decoder ifcoding is used) for transmitted substream i may be expressed as anon-linear, unknown function ƒ of the set of SINR_(k), k=1, . . . ,N_(t), for example:BER _(i)=ƒ({SINR_(k) ^(i)}),i=1, . . . , N;k=1, . . . , N _(t)

Next, the function ƒ is approximated by some known function.Specifically, the output BER is approximated by the average of the biterror rate over the channel, for example:

$\begin{matrix}{{\overset{\_}{BER}}_{i} \approx {{1/N_{t}}\;{\sum\limits_{k = 1}^{N_{t}}{BER}_{k}^{i}}}} & (1.)\end{matrix}$where BER_(k) ^(i) is the bit error rate given the SINR at tone k forspatially-multiplexed substream i. In another example, BER_(k) can alsobe the bit error rate given the signal-to-noise ratio at tone k. Theaverage may also be taken in the time domain where BER_(k) is the biterror rate given the SINR at channel time sample k. BER_(k) may be thebit error rate with respect to a given signal component (e.g., a signaltone or tap delay).

Furthermore, BER_(k) is also approximated by some simple closed-formfunction. Through simulations it has been found that for mode 1 of802.1-1a (e.g., BPSK, R1/2), the behavior of the average bit error rateBER with respect to the SINR or SNR (in some examples, the BERnormalization factor 1/N_(t) may be omitted, since it does not affectthe antenna selection) can be modeled, for example, by:

$\begin{matrix}{{{{\overset{\_}{BER}}_{i} \approx {- {\sum\limits_{k = 1}^{N_{t}}{\tanh\left( {SINR}_{k}^{i} \right)}}}};{i = 1}},\ldots\mspace{11mu},N} & (2.)\end{matrix}$The BER at signal component k has been approximated by −tan h(SINR_(k)).

The tan h function may not always adequately approximate the BER,particularly for different modulation techniques. Some of the followingfunctions may generally afford better approximations when usingparticular techniques:

1) The BER of an uncoded BPSK modulation in AWGN channel is (see, e.g.,J. G. Proakis, Digital Communications, 3^(rd) Ed. McGraw-Hill Series,1995)

${BER}_{BPSK} = {{Q\left( \sqrt{\frac{2E_{b}}{N_{o}}} \right)} = {{Q\left( \sqrt{2\;\gamma_{b}} \right)} = {{\frac{1}{2}{{erfc}\left( \sqrt{\gamma_{b}} \right)}} = {\frac{1}{2}{{{erfc}\left( \sqrt{\gamma_{s}} \right)}.}}}}}$The shape of the function erfc is reasonably approximated by thefunction (as compared to y=−tan h(x))y=−[(1−e ^(−2√{square root over (x)}))+(1−e ^(−1.8x))]

2) The BER of an uncoded QPSK modulation in AWGN channel is (see, e.g.,J. G. Proakis, Digital Communications, 3^(rd) Ed. McGraw-Hill Series,1995)

${BER}_{QPSK} = {{Q\left( \sqrt{\frac{2E_{b}}{N_{o}}} \right)} = {{Q\left( \sqrt{2\;\gamma_{b}} \right)} = {{\frac{1}{2}{{erfc}\left( \sqrt{\gamma_{b}} \right)}} = {\frac{1}{2}{{{erfc}\left( \sqrt{\frac{\gamma_{s}}{2}} \right)}.}}}}}$The shape of erfc(√{square root over (x/2)}) is better approximated bythe function:y=−[(1−e ^(−1.3√{square root over (x)}))+(1−e ^(−x))]than by y=−tan h(x).

3) The BER of an uncoded 16QAM modulation in AWGN channel may be derivedfrom the symbol error rate (SER) given, for example, in J. G. Proakis,Digital Communications, 3^(rd) Ed. McGraw-Hill Series, 1995 as

${BER}_{16{QAM}} = {{1 - \sqrt{1 - {\frac{3}{2}{Q\left( \sqrt{\frac{3E_{s}}{15N_{o}}} \right)}}}} = {1 - \sqrt{1 - {\frac{3}{4}{{erfc}\left( \frac{\gamma_{s}}{10} \right)}}}}}$An appropriate fitting function is y=−(1−e^(−0.2x)).

4) The BER of an uncoded 64QAM modulation in AWGN channel may be derivedfrom the symbol error rate (SER) given, for example, in J. G. Proakis,Digital Communications, 3^(rd) Ed. McGraw-Hill Series, 1995 as

$\begin{matrix}{{BER}_{64{QAM}} = {1 - \left( {1 - {\frac{7}{4}{Q\left( \sqrt{\frac{\gamma_{s}}{21}} \right)}}} \right)^{\frac{1}{3}}}} \\{= {1 - \left( {1 - {\frac{7}{8}{{erfc}\left( \sqrt{\frac{\gamma_{s}}{42}} \right)}}} \right)^{\frac{1}{3}}}}\end{matrix}$An appropriate fitting function isy=−(1−e^(−0.35√{square root over (x)})).

It is to be understood than any fitting function that reasonably modelsthe behavior of the BER versus SINR can be used in equation (2). Thenumber of appropriate fitting functions is not limited to the fewexamples given above.

As mentioned above, steps 406 to 410 are iteratively performed until allpossible combinations of subsets of antennas are considered (step 411).At the conclusion of this iterative process, a set of N estimates of BERvalues (one for each spatially-multiplexed signal) for all

$\frac{M!}{{n!}{\left( {M - n} \right)!}}\mspace{14mu}\left( {{or}\mspace{14mu}\left( \frac{M!}{{n!}{\left( {M - n} \right)!}} \right)^{2}} \right)$possible antennas combinations is obtained. It then remains to selectthe subset of antennas that minimize the mean over the set of BERs, themaximum over the set of BERs or, the minimum of the set of BERs (step412).

$\begin{matrix}{\min\limits_{\underset{combinations}{antennas}}\left\{ {\underset{{i = 1},\ldots\;,N}{mean}\left\{ {BER}_{i} \right\}} \right\}} \\{\min\limits_{\underset{combinations}{antennas}}\left\{ {\min\limits_{{i = 1},\ldots\;,N}\left\{ {BER}_{i} \right\}} \right\}} \\{\min\limits_{\underset{combinations}{antennas}}\left\{ {\max\limits_{{i = 1},\ldots\;,N}\left\{ {BER}_{i} \right\}} \right\}}\end{matrix}$

FIG. 4B is a flowchart of an antenna selection algorithm 500 in whichthe coding/modulation mode may be changed as frequently as once perpacket realization in response to corresponding changes in the channel318. In this example, the coding/modulation mode is adapted at the samerate as antenna selection is effected.

Referring to FIG. 4B, steps 501 and 502 are similar to steps 401 and402, respectively. As shown, steps 504 through 510 comprise a loop thatis iteratively executed until all possible combinations of subsets ofantennas have been evaluated. It follows that the number of iterationsof this loop is equivalent to

$\frac{M!}{{n!}{\left( {M - n} \right)!}}$(e.g., selection at one end of the link) or

$\left( \frac{M!}{{n!}{\left( {M - n} \right)!}} \right)^{2}$(e.g., selection at both ends of the link). In this regard steps 504 and506 are similar to steps 406 and 408, respectively. Based upon theknowledge of the instantaneous SINR at all tones, a link adaptationblock determines the most efficient mode for each spatially-multiplexedsignal, given a mode selection criterion (e.g., a maximum data rate anda minimum transmit power) (step 508). This step is similar to step 404,with the exception that the mode decision is made based uponinstantaneous SNR (or SINR) statistics rather than upon long-term SNR(or SINR) statistics. As a result, different combinations of subsets ofantennas may yield different mode decisions. Finally, given theinstantaneous SINR and mode information, step 510 computes or determinesthe corresponding BER in the same manner as was described above withreference to step 410.

Again, steps 504 through 510 are performed until all possiblecombinations of subsets of antennas are considered (step 511). Once thishas occurred, a set of N estimates of BER values (e.g., one for eachspatially-multiplexed signal) for all

$\frac{M!}{{n!}{\left( {M - n} \right)!}}\mspace{14mu}\left( {{or}\mspace{14mu}\left( \frac{M!}{{n!}{\left( {M - n} \right)!}} \right)^{2}} \right)$possible antennas combinations is obtained. The selection algorithm 500differs from the algorithm 400 in that the

$\frac{M!}{{n!}{\left( {M - n} \right)!}}\mspace{14mu}\left( {{or}\mspace{14mu}\left( \frac{M!}{{n!}{\left( {M - n} \right)!}} \right)^{2}} \right)$possible antennas combinations do not necessarily use the samecoding/modulation mode. The decision of which antennas subset to selecttherefore depends not only on a minimization of the BER but also on themode (e.g., data rate or throughput). Several exemplary options areprovided with regard to the final decision of selecting a subset ofantenna elements pursuant to step 512 of the selection algorithm 500:

Option 1

-   -   1) Group all combinations of subsets of antennas using the same        mode into a common pool.    -   2) Choose the pool corresponding to the highest mode (yielding        maximum data rate).    -   3) Within that pool, select the combination of subset of        antennas that minimizes the BER in a manner substantially        similar to that described with reference to Step 412.

Option 2

-   -   Regardless of which mode is used by each combination, select the        combination of antenna subsets that minimizes the BER in a        manner substantially similar to that described with reference to        Step 412.

Option 3

Implement a hybrid version of option 1 and 2, for example:

-   -   1) Group all combinations of subsets of antennas using the same        mode into a common pool.    -   2) Choose the X pools corresponding to the X highest modes        (yielding maximum data rate), where X is an integer equal to 1,        or 2 or 3, etc.    -   3) Within these pools, select the combination of subset of        antennas that minimizes the BER in a manner substantially        similar to that described with reference to step 412.

FIG. 5 illustratively represents the packet error rate (PER) as functionof SNR resulting from employment of an exemplary antenna selectiontechnique within a SM-MIMO-OFDM system operative in a noise-limitedenvironment. The results of FIG. 5 may be applicable, for example, to asystem using four transmit and receive antennas in the mannerexemplified by FIG. 3. The results reflect, as merely exemplaryexamples, a packet size of 1000 bytes and a fixed coding/modulationmode. The results also reflect that two exemplary RF chains areincorporated within both the applicable transmitter and receiver. Inaddition, the results of FIG. 5 use BPSK modulation, a coding rate of1/2 (e.g., mode 1 of 802.11a), a channel model characterized as “channelA” (e.g., 50 ns rms delay spread, 0.5 antenna correlation), and afitting function of tan h.

The legend for the curves in FIG. 5 is as follows:

2×2 2SM-MIMO MMSE: This system corresponds to a SM-MIMO-OFDM systemusing 2 transmit and 2 receive antennas together with 2spatially-multiplexed (SM) signals. Since the number of antennas isequal to the number of SM signals, no antenna selection is applied. Abaseband combining arrangement is used at the receiver to separate thetwo substreams, e.g., MMSE.

4×4 2SM-MIMO sel mcap MMSE: This system corresponds to a SM-MIMO-OFDMsystem using 4 transmit and 4 receive antenna elements together with 2spatially-multiplexed (SM) signals. A conventional selection method isapplied at both the transmitter and receiver to select a subset of 2antenna elements among four, according to a maximum capacity criterion.After the selection at the receiver, MMSE is applied at baseband toseparate the two substreams.

2×4 2SM-MIMO sel mber MMSE (bound): This system corresponds to aSM-MIMO-OFDM system using 2 transmit and 4 receive antenna elementstogether with 2 spatially-multiplexed (SM) signals. A selection methodis applied only at the receiver end to select a subset of 2 antennaelements among four, according to the minimum BER criterion. In thiscase, no fitting function is used to approximate the BER. Instead, theBER is assumed to be known perfectly. This case may not be readilyimplemented, but rather provides a bound on the performance which may beachieved through use of some embodiments according to some aspects ofthe present invention.

4×4 2SM-MIMO sel mber MMSE (bound) This system corresponds to aSM-MIMO-OFDM system using 4 transmit and 4 receive antenna elementstogether with 2 spatially-multiplexed (SM) signals. A selection methodis applied at both transmit and receive sides to select a subset of 2antenna elements among four, according to the minimum BER criterion. Inthis case, no fitting function is used to approximate the BER. Instead,the BER is assumed to be known perfectly. This case may not be readilyimplemented, but rather provides a bound on the performance which may beachieved through use of some embodiments according to some aspects ofthe present invention.

4×4 2SM-MIMO sel mber MMSE (implementation tan h) This systemcorresponds to a SMMIMO-OFDM system using 4 transmit and 4 receiveantenna elements together with 2 spatially-multiplexed (SM) signals. Aselection method according to some embodiments according of the presentinvention is applied at both transmit and receive sides to select asubset of 2 antenna elements among four, according to a minimum BERcriterion. The fitting function to approximate the BER is tan h.

The results illustratively represented by FIG. 5 show that all systemsusing some type of antenna selection provide gains relative to systemswith no selection, and that antenna selection based upon minimum BERprovides significantly more gain than selection based upon the maximumcapacity criterion. Specifically, at a PER level of 10e-2 and withantenna selection in accordance with the present invention being appliedat both the transmitter and receiver, a 7.6 dB gain is achieved relativeto a system with no selection and 4.2 dB gain is demonstrated relativeto a system in which selection is based on maximum capacity. Whenselection is applied consistent with some embodiments according to someaspects of the present invention at only the receiver, the resultingperformance is seen to be between that achieved when no selection isemployed and that which occurs when selection is employed at both thetransmitter and receiver. Finally, the performance of the system inaccordance with some embodiments according to some aspects of thepresent invention very closely approaches a theoretical performancebound illustrated by FIG. 5.

C. Antenna Selection in a SC-MIMO-OFDM System

FIG. 6 illustrates a SC-MIMO-OFDM system 600 which utilizes precodingtechniques in addition to an exemplary antenna selection methodaccording to some embodiments of the present invention. In theembodiment of FIG. 6, precoding refers to various baseband weighting andcombining arrangements performed at a transmitter 602. Referring to FIG.6, a single-stream of symbols 604 is weighted by a set of complexcoefficients 608 and combined to produce a set of N output signals whereN refers to the number of RF chains 612 used within the transmitter 602.These N output signals are then passed through the N RF chains 612 inorder to produce N RF signals. These N RF signals are then coupled to acorresponding group of N of M transmit antenna elements 616 via a switch620 and transmitted through a channel 624.

At a receiver 622, a set of N of M receive antenna elements 626 isselected via a switch 630 to receive the incoming signals communicatedthrough a channel 624. The N RF receive signals are then processed by NRF chains 634 and converted to the digital domain for basebandprocessing to recover the original transmitted signal.

Some embodiments according to some aspects of the present invention mayprovide, for example, that the baseband weights 608 and antennaselection method are designed to collectively contribute to theminimization of the BER. Some embodiments according to some aspects ofthe present invention may provide, for example, that the basebandweights 608 may be chosen to maximize the output SNR (or SINR) orcapacity, while the antenna selection is conducted so as to minimize theBER. The right and left singular vectors of the sub-channel matrix{tilde over (H)}_(k) corresponding to the largest singular value may beused to select optimal subsets of transmit antenna elements 616 andreceive antenna elements 626 as well as the appropriate transmitbaseband weights 608 and receive baseband weights 640. Determination ofbaseband weighting values in the context of MIMO systems lacking antennaselection has been described, for example, in J. B. Andersen, IEEEAntennas and Propagation Magazine, vol. 42, no. 2, April 2000, pp.12-16, which is incorporated herein by reference in its entirety.

The exemplary embodiment illustrated in FIG. 6 may be modified byreplacing the baseband weights 608 within the transmitter 602 by aspace-time coding block. In this case, an antenna selection method maybe employed to select the subset of antennas in both the transmitter andreceiver in accordance with some embodiments of the present invention.In addition, the space-time coding block processes the input stream ofsymbols as described in, for example, “A simple transmit diversitytechnique for wireless communications”, by S. M. Alamouti, IEEE Journalon Selected Areas in Communications, vol. 16, issue 8, October 1998,pages 1451-1458, which is incorporated herein by reference in itsentirety.

D. Antenna Selection in a DS-SS-SIMO System

FIG. 7 depicts a receiver 700 of a DS-SS SIMO system having two receiveantenna elements 704 (n_(R)=2). The receiver 700 integrates RAKEreceiver functionality together with an exemplary antenna selectionprocess. As shown, the receiver 700 is equipped with only a single RFchain 708 disposed to be connected to only one of the two receiveantenna elements 704 at any given time via a switch 712. The choice ofwhich of the two elements 704 to connect to the RF chain 708 is madebased upon the minimum BER criterion. Some embodiments according to someaspects of the present invention may provide that the received signalBER corresponding to each receive antenna element 704 is computed andthe element 704 yielding the minimum value of BER is selected. Since theBER may typically comprise a complicated function of the applicablechannel and of the coding/modulation and antenna combining techniquesused, the BER for a given channel and antenna combining technique isapproximated such that it varies as a function of the coding/modulationmethod used.

Once the optimal one of the antenna elements 704 has been selected, theRAKE receiver behaves in the same way as if it were implemented in asingle-input single-output (SISO) system (e.g., one antenna at each endof the link). The RAKE receiver uses a plurality of J correlators 720(e.g., J=2 in FIG. 7), each of which corresponds to one of the first Jseparable multipath components. Each such multipath component isassociated with a time delay τ_(j), j=1, . . . ,J, respectively. Theoutput of each correlator 720 (e.g., a finger) is then weighted 730 andcombined 740 to form a single output received signal 750 comprising anestimate of the transmitted signal.

In one exemplary example, the received signal corresponding to thei^(th) antenna element 704 at the input of the RAKE receiver may beexpressed as:

$\begin{matrix}{{r_{i}(t)} = {{\sum\limits_{l = 1}^{L_{i}}{h_{i,l}\sqrt{2\; P}{d\left( {t - \tau_{i,l}} \right)}{p\left( {t - \tau_{i,l}} \right)}\;{\cos\left( {{w_{0}\left( {t - \tau_{i,l}} \right)} - \theta_{i,l}} \right)}}} + {n_{i}(t)}}} & (3.)\end{matrix}$where L_(i) is the number of taps in the channel received at the i^(th)antenna element 704, h_(i,l) is the complex channel gain at antenna iand tap l, P is the signal transmit power, d is the data sequencecomprised of symbols of period T, and p is the spreading sequencecomposed of chips of period T_(c)=T/G, where G is the spreading factor.In addition, τ_(i,l) is the path delay associated with tap l and antennai, w₀ corresponds to the carrier frequency w₀=2πf₀, and θ_(i,l) is thephase shift corresponding to tap l and antenna i. The noise n_(i)measured at the i^(th) antenna element 704 is modeled as an AWGN processwith two-side spectral density N₀/2. For the sake of simplicity andclarity of expression, equation (3) assumes a single-user environment.However, the present invention need not be so limited and alsocontemplates being applied in the presence of multiple users.

At the output of the correlator 720 of the j^(th) finger, the receivedsignal may be represented as:

$\begin{matrix}{r_{i,j} = {{\sqrt{\frac{2}{T}}{\int_{\tau_{j}}^{\tau_{j}}{{r_{i}(t)}{p\left( {t - \tau_{j}} \right)}\;{\cos\left( {{w_{0}\left( {t - \tau_{j}} \right)} - \theta_{j}} \right)}{\mathbb{d}t}}}} = {{\sqrt{P\; T}h_{i,j}d_{0}} + n_{i,j}}}} & (4.)\end{matrix}$where d₀ is the desired symbol to be demodulated, and n_(i,j) is theAWGN noise component with zero-mean and with two-side spectral densityN₀/2. Again for purposes of simplicity and clarity of presentation, itwas assumed in equation (4) that there is no interpath interference(IPI). However, the present invention also contemplates being used inthe presence of IPI.

Following diversity combining, the final output of the RAKE receivercorresponding to the i^(th) antenna element 704 is:

$\begin{matrix}{r_{i} = {\sum\limits_{j = 1}^{J}{w_{i,j}r_{i,j}}}} & (5.)\end{matrix}$where J is the number of RAKE fingers and where the optimum combiningweights are generally chosen so as to match the channel, for example:w _(i,j) =h* _(i,j)  (6.)

In this case, the RAKE performs maximum ratio combining and the SNR atthe RAKE output, corresponding the i^(th) antenna element 704 is givenby

$\begin{matrix}{\gamma_{i} = {\sum\limits_{j = 1}^{J}\;\gamma_{i,j}}} & (7.)\end{matrix}$where γ_(i,j) is the post-combining SNR on the j^(th) path associatedwith the i^(th) antenna element 704. Based on (4), γ_(i,j) may beexpressed by:

$\begin{matrix}{{\gamma_{i,j} = \frac{{h_{i,j}}^{2}P}{\sigma^{2}}}{{{where}\mspace{14mu}\sigma^{2}} = {{\frac{N_{0}}{2} \cdot \frac{2}{T}}\mspace{14mu}{\text{is~~~the~~~noise~~~power}.}}}} & (8.)\end{matrix}$

The BER at the output of the RAKE receiver corresponding to the i^(th)antenna element 704 may be obtained from the knowledge of theprobability density function (PDF) of γ_(i). For example, if no codingis used and BPSK modulation is applied to the data sequence inaccordance with the methodology described, for example, in “DigitalCommunications”, J. G. Proakis, 3^(rd) Edition, McGraw-Hill Series,1995, the BER is found by integrating the conditional error probabilityrepresented by Q(√{square root over (2γ_(i))}) over the PDF of γ_(i),for example:

$\begin{matrix}{{BER}_{i} = {\int_{0}^{\infty}{{Q\left( \sqrt{2\gamma_{i}} \right)}{p_{\gamma}\left( \gamma_{i} \right)}\ {\mathbb{d}\gamma_{i}}}}} & (9.)\end{matrix}$

Once the BER is estimated for all receive antennas, the antenna element704 yielding the minimum BER is selected:

$\begin{matrix}{\min\limits_{{i = 1},{\ldots\mspace{11mu} n_{R}}}\left\{ {BER}_{i} \right\}} & (10.)\end{matrix}$where n_(R) represents the total number of receiver antenna elements.

As will be readily appreciated, as coding is added to the system (e.g.,turbo coding, convolution coding) and other modulation levels are used,the modeling function used in (9) to estimate the BER will need tochange. Some embodiments according to some aspects of the presentinvention may provide that any fitting function which accurately modelsBER behavior for a given system may be used by an exemplary antennaselection algorithm. The fitting function will generally be dependentupon parameters including, for example, one or more of the following:the channel, coding and modulation used, signal processing at transmitand/or receiver side, receiver SNR and other parameters.

The exemplary embodiment illustrated in FIG. 7 may be extended to atwo-dimensional RAKE receiver in which processing is conducted in boththe space and time domain. In this context, an exemplary antennaselection algorithm may be incorporated to select a subset of N antennas(N>1), from a total of M antennas (M>N), which minimize the BER at theoutput of the 2D-RAKE.

While the present invention has been described with reference to certainembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted withoutdeparting from the scope of the present invention. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the present invention without departing from its scope.Therefore, it is intended that the present invention not be limited tothe particular embodiments disclosed, but that the present inventionwill include all embodiments falling within the scope of the appendedclaims.

1. A method for selecting a subset of receive antennas of a receiver toreceive a transmitted RF signal, comprising: establishing possiblesubsets of the receive antennas; determining sets of channel parameterstatistics corresponding to the possible subsets of the receiveantennas; computing output bit error rates of the receiver, each outputbit error rate being computed based on at least one set of channelparameter statistics; selecting a particular possible subset of thereceive antennas based upon a criterion predicated on the computedoutput bit error rates; and connecting one or more RF chains of thereceiver to the receive antennas of the selected particular possiblesubset, wherein each set of channel parameter statistics is computedover a frequency domain.
 2. The method according to claim 1, furthercomprising: selecting transmission modes, each transmission mode beingselected based on at least one set of channel parameter statistics; andpredicating the criterion on at least the selected transmission modes.3. The method according to claim 2, wherein each selected transmissionmode comprises a modulation level and a coding rate.
 4. The methodaccording to claim 1, wherein each set of channel parameter statisticscomprises at least one of an output signal-to-noise ratio, an outputsignal-to-interference-and-noise ratio, a log-likelihood ratio and aEuclidian distance in a signal constellation of the receiver.
 5. Themethod according to claim 1, wherein each set of channel parameterstatistics comprises at least one of a first-order statistic, asecond-order statistic and a higher-order statistic.
 6. The methodaccording to claim 1, wherein each set of channel parameter statisticsis computed over a time domain.
 7. The method according to claim 1,wherein the criterion is based on a minimization of the output bit errorrates.
 8. The method according to claim 1, wherein the criterion isbased on at least one of a maximization of a data rate within a firststage of the receiver and a minimization of the output bit error ratesin a second stage of the receiver.
 9. The method according to claim 1,wherein at least one of the output bit error rates is approximated by aclosed-form expression.
 10. The method according to claim 9, whereineach output bit error rate is approximated by a closed-form expression.11. The method according to claim 9, wherein the closed-form expressioncomprises at least one of a) y=−tan h(x), b)y=−[(1−e^(−2√{square root over (x)}))+(1−e^(−1.8x))], c)y=−[(1−e^(−1.3√{square root over (x)}))+(1−e^(−x))], d)y=−(1−e^(−0.2x)), and e) y=−(1−e^(−0.35√{square root over (x)})). 12.The method according to claim 9, wherein the closed-form expression isdependent upon at least one of coding and modulation of the transmittedRF signal.
 13. The method according to claim 9, wherein the closed-formexpression is a function of an output signal-to-noise ratio or an outputsignal-to-noise-and-interference ratio of the receiver.
 14. The methodaccording to claim 1, wherein the receive antennas are greater in numberthan the number of RF chains, and wherein the number of receive antennasin each possible subset is equal to the number of the RF chains.
 15. Themethod according to claim 1, wherein the transmitted RF signal comprisesat least one of a code division multiple access signal, a single carriersignal, an orthogonal frequency division multiplexed signal and a UWBsignal.
 16. A method for selecting a subset of transmit antennas of atransmitter to transmit an RF input signal as a plurality of RF outputsignals that are subsequently received by a receiver, comprising:establishing possible subsets of the transmit antennas; determining setsof channel parameter statistics corresponding to the possible subsets ofthe transmit antennas; selecting transmission modes respectivelycorresponding to the sets of channel parameter statistics, whereinselecting transmission modes comprises selecting a particular modulationtype from a plurality of available modulation types and selecting aparticular coding rate from a plurality of available coding rates;computing output bit error rates of the receiver, each output bit errorrate being computed based on at least one set of channel parameterstatistics and at least one selected transmission mode; selecting aparticular possible subset of the transmit antennas based on a criterionpredicated on at least the computed output bit error rates; andconnecting one or more RF chains of the transmitter to the transmitantennas of the selected particular possible subset.
 17. The methodaccording to claim 16, wherein each set of channel parameter statisticscomprises at least one of an output signal-to-noise ratio, an outputsignal-to-interference-and-noise ratio, a log-likelihood ratio, and aEuclidian distance in a signal constellation of the receiver.
 18. Themethod according to claim 16, wherein each set of channel parameterstatistics comprises at least one of a first-order statistic, asecond-order statistic and a higher-order statistic.
 19. The methodaccording to claim 16, wherein each set of channel parameter statisticsis computed over a frequency domain.
 20. The method according to claim16, wherein each set of channel parameter statistics is computed over atime domain.
 21. The method according to claim 16, wherein the criterionminimizes the output bit error rates of the receiver.
 22. The methodaccording to claim 16, wherein the criterion is predicated on thecomputed output bit error rates and the selected transmission modes. 23.The method according to claim 16, wherein the criterion is predicated onat least one of a maximization of a data rate in a first stage of thereceiver and a minimization of the output bit error rates in a secondstage of the receiver.
 24. The method according to claim 16, whereineach output bit error rate is approximated by a closed-form expression.25. The method according to claim 24, wherein the closed-form expressioncomprises at least one of a) y=−tan h(x), b)y=−[(1−e^(−2√{square root over (x)}))+(1−e^(−1.8x))], c)y=−[(1−e^(−1.3√{square root over (x)}))+(1−e^(−x))], d)y=−(1−e^(−0.2x)), and e) y=−(1−e^(−0.35√{square root over (x)})). 26.The method according to claim 24, wherein the closed-form expression isdependent on at least one of a coding and a modulation of the RF outputsignals.
 27. The method according to claim 24, wherein the closed-formexpression is a function of at least one of an output signal-to-noiseratio or an output signal-to-noise-and-interference ratio of thereceiver.
 28. The method according to claim 16, wherein the plurality ofRF output signals comprise at least one of a code division multipleaccess signal, a single carrier signal, an orthogonal frequency divisionmultiplexed signal and a UWB signal.
 29. The method according to claim16, wherein the transmit antennas are greater in number than the numberof RF chains, and wherein the number of transmit antennas in eachpossible subset equals the number of the RF chains.
 30. In acommunication system comprising a transmitter and a receiver, thetransmitter comprising transmit antennas adapted to transmit a set ofspatially-multiplexed RF output signals through a channel using two ormore transmit RF chains, the receiver comprising receive antennasadapted to receive the set of spatially-multiplexed RF output signalsand adapted to responsively generate a set of spatially-multiplexedreceived RF signals that is processed by two or more receive RF chains,an antenna selection method comprising: establishing possible subsets ofthe transmit antennas and possible subsets of the receive antennas;determining sets of channel parameter statistics corresponding tocombinations of the possible subsets of the transmit antennas and thepossible subsets of the receive antennas; selecting transmission modesrespectively corresponding to the sets of channel parameter statistics,wherein selecting transmission modes comprises selecting a particularmodulation type from a plurality of available modulation types andselecting a particular coding rate from a plurality of available codingrates; computing output bit error rates of the receiver, each output biterror rate being computed based on at least one set of channel parameterstatistics and a corresponding selected transmission mode; selecting aparticular possible subset of the transmit antennas and a particularpossible subset of the receive antennas based on a criterion predicatedon at least the computed output bit error rates; connecting the two ormore of the transmit RF chains to the selected particular possiblesubset of the transmit antennas; and connecting the two or more receiveRF chains to the selected particular possible subset of the receiveantennas.
 31. The method according to claim 30, wherein each set ofchannel parameter statistics comprises at least one of an outputsignal-to-noise ratio, an output signal-to-interference-and-noise ratio,a log-likelihood ratio and a Euclidian distance in signal constellationof the receiver.
 32. The method according to claim 30, wherein each setof channel parameter statistics comprises at least one of a first-orderstatistic, a second-order statistic and a higher-order statistic. 33.The method according to claim 30, wherein each set of channel parameterstatistics is computed over a frequency domain.
 34. The method accordingto claim 30, wherein each set of channel parameter statistics iscomputed over a time domain.
 35. The method according to claim 30,wherein the criterion is based on a minimization of the output bit errorrates.
 36. The method according to claim 30, wherein the criterion ispredicated on the computed output bit error rates and the selectedtransmission modes.
 37. The method according to claim 30, wherein thecriterion is based on at least one of a maximization of a data ratewithin a first stage of the receiver and a minimization of the outputbit error rates in a second stage of the receiver.
 38. The methodaccording to claim 30, wherein the output bit error rates areapproximated by one or more closed-form expressions.
 39. The methodaccording to claim 38, wherein the one or more closed-form expressioncomprises at least one of a) y=−tan h(x), b)y=−[(1−e^(−2√{square root over (x)}))+(1−e^(−1.8x))], c)y=−[(1−e^(−1.3√{square root over (x)}))+(1−e^(−x))], d)y=−(1−e^(−0.2x)), and e) y=−(1−e^(−0.35√{square root over (x)})). 40.The method according to claim 38, wherein the one or more closed-formexpressions depend on at least one of a coding and a modulation of theset of spatially-multiplexed RF output signals.
 41. The method accordingto claim 38, wherein the one or more closed-form expressions arefunctions of at least one of an output signal-to-noise ratio and anoutput signal-to-noise-and-interference ratio of the receiver.
 42. Themethod according to claim 30, further comprising: performing a splittingand a weighting operation on baseband input signals using a set ofbaseband weighting values to form a first set of baseband signals; andgenerating the set of spatially-multiplexed RF output signals based onat least the first set of baseband signals.
 43. The method according toclaim 30, further comprising: downconverting the set ofspatially-multiplexed received RF signals to form a first set ofbaseband signals; and performing a baseband weighting and a combiningoperation on the first set of baseband signals using a set of basebandweighting values.
 44. The method according to claim 30, wherein the setof spatially-multiplexed RF output signals comprises at least one of acode division multiple access signal, a single carrier signal, anorthogonal frequency division multiplexed signal and a UWB signal. 45.The method according to claim 30, wherein the transmit antennas aregreater in number than the two or more transmit RF chains, and whereinthe receive antennas are greater in number than the two or more receiveRF chains.
 46. In a communication system comprising a transmitter and areceiver, the transmitter comprising transmit antennas adapted totransmit a set of RF output signals through a channel using one or moretransmit RF chains, the receiver comprising receive antennas adapted toreceive the set of RF output signals and adapted to responsivelygenerate a set of received RF signals that is processed by one or morereceive RF chains, an antenna selection method comprising: establishingpossible subsets of the transmit antennas and possible subsets of thereceive antennas; determining sets of channel parameter statisticscorresponding to combinations of the possible subsets of the transmitantennas and the possible subsets of the receive antennas; selectingtransmission modes respectively corresponding to the sets of channelparameter statistics, wherein selecting transmission modes comprisesselecting a particular modulation type from a plurality of availablemodulation types and selecting a particular coding rate from a pluralityof available coding rates; computing output bit error rates of thereceiver, each output bit error rate being computed based on at leastone set of channel parameter statistics and a corresponding selectedtransmission mode; selecting a particular possible subset of thetransmit antennas and a particular possible subset of the receiveantennas based on a criterion predicated on at least the computed outputbit error rates; connecting the one or more of the transmit RF chains tothe selected particular possible subset of the transmit antennas; andconnecting the one or more receive RF chains to the selected particularpossible subset of the receive antennas.
 47. The method according toclaim 46, wherein the criterion is predicated on the computed output biterror rates and the selected transmission modes.
 48. The methodaccording to claim 46, further comprising: performing a splitting and aweighting operation on an input baseband signal using a set of transmitbaseband weighting values to form a first set of baseband signals; andgenerating the RF output signals based on at least the first set ofbaseband signals.
 49. The method according to claim 48, wherein the setof transmit baseband weighting values are generated using precoding orspace-time coding techniques.
 50. The method according to claim 46,further comprising: downconverting the set of received RF signals toform a first set of baseband signals; and performing a basebandweighting and a combining operation on the first set of baseband signalsusing a set of receive baseband weighting values.
 51. The methodaccording to claim 48, wherein the set of transmit baseband weights areobtained from a singular vector of a channel matrix corresponding to theselected particular possible subset of the transmit antennas.
 52. Themethod according to claim 50, wherein the set of receive basebandweights are obtained from a singular vector of a channel matrixcorresponding to the selected particular possible subset of the receiveantennas.